1. IV.4 Signal-to-Noise Ratios
Background
Example

2. Background Motivation
Wouldn’t it be Nice to Have a Single Performance Measure that Simultaneously Identified Factor Settings that
Optimally target the mean
Reduce variation
This is the Major Motivation Underlying Taguchi’s Use of Signal-to-Noise Ratios.

3. Background Some Popular S/N Ratios
Taguchi proposed OVER 80 signal-to-noise (S/N) ratios. The following three are among his most widely applicable. Our goal is to MAXIMIZE all three.
SNs = -10 log(Sy2/n)
What are the optimal values for yi?
Used when “smaller is better”
SNL = -10 log(S(1/y2)/n)
Used when “larger is better”
SNT = 10 log(y2/s2)
Ostensibly used when “target is better”
How does SNT measure proximity to target?
Skim for now

4. Background Criticisms of Taguchi’s S/N Ratios
SNs and SNL
y will almost always be a more sensitive measure of the size of effects on the mean
SNT
If y and s are independent, we can look at them separately to make better decisions
y and s are frequently directly related, a situation SNT will not detect
Instead of SN(T), could also use (ybar-t)^2 + s^2 (quadratic loss function)

5. Example 6 Growing an Epitaxial Layer on Silicon Wafers Figure 12 - Wafers Mounted on Susceptor
Kacker, R. N. and Shoemaker, A. C. (1986). “Robust Design: A Cost-Effective Method for Improving Manufacturing Processes” AT&T Technical Journal 65, pp

6. Example 6 Growing an Epitaxial Layer on Silicon Wafers Figure 13 - Initial and Test Settings
The response variable is thickness of epitaxial layer in mm with a target of 14.5 mm. Which factors will affect
mean?
variation?

7. Example 6 Growing an Epitaxial Layer on Silicon Wafers Figure 14 - The Experimental Design
Each experimental run results in 70 observations on the response!

8. Example 6 Growing an Epitaxial Layer on Silicon Wafers The Experimental Design
Note that the design here is “non-standard”
Can you assign factors to columns A, B, C, and D in the 16-run signs table?
Hint: the original factors A, B, C and D cannot be used to generate the design
Which columns would the other 4 factors be assigned to in the 16-run signs table?
Show 16-run signs table. Assign A to D, B to C, and C to B, E to D. D=-ABC, F=ABD, G=ACD and H=BCD. This is still a Resolution IV design.

9. Example 6 - Analysis Using Only SNT Growing an Epitaxial Layer on Silicon Wafers Figure 16a - Completed Response Table
Doesn’t show entire table. Open Excel sheet.

10. Example 6 - Analysis Using Only SNT Growing an Epitaxial Layer on Silicon Wafers Figure 17 - Effects Normal Probability Plot

11. Example 6 - Analysis Using Only SNT Growing an Epitaxial Layer on Silicon Wafers Interpretation
What factors favorable affect SNT?
A (susceptor rotation method) set at continuous
H (nozzle position) set at 6.

12. Example 6 Analysis Using Mean and Log(s) Growing an Epitaxial Layer on Silicon Wafers Figure 18a - Response Table for Mean

13. Example 6 Analysis Using Mean and Log(s) Growing an Epitaxial Layer on Silicon Wafers Figure 19a - Response Table for Log(s)

14. Example 6 Analysis Using Mean and Log(s) Growing an Epitaxial Layer on Silicon Wafers Figure 20 - Effects Normal Probability Plot for Mean

15. Example 6 Analysis Using Mean and Log(s) Growing an Epitaxial Layer on Silicon Wafers Figure 21 - Effects Normal Probability Plot for Log(s)
Note D

16. Example 6 Analysis Using Mean and Log(s) Growing an Epitaxial Layer on Silicon Wafers Interpretation
What factors affect the mean?
D (deposition time) set at high level increases the mean.
What factor settings favorably affect variability?
A (susceptor rotation method) set at continuous.
H (nozzle position) set at 6.
D (deposition time) set at low.
Why did SN(T) miss D?

17. Example 6 Analysis Growing an Epitaxial Layer on Silicon Wafers Interpretation
Conclusions:
Set nozzle position at 6
Use continuous susceptor rotation method
Use deposition time to adjust mean to target